O objetivo desta tese é oferecer um arcabouço que permita a modelagem de simetrias em fibrados suaves, que possuam um bom comportamento local. Para tanto, usa-se ferramentas de grupoides de Lie e correlatas, com a finalidade de reduzir, quando possível, simetrias dadas pela ação de um grupo diferenciável, possivelmente de dimensão infinita, sobre um fibrado suave, a problemas em dimensão finita. Uma definição de invariância de uma forma diferencial, definida no espaço total de um fibrado suave, sob a ação de um grupoide de Lie, é apresentada e desenvolvida. A seguir, discute-se estas ferramentas no contexto da formulação lagrangiana da teoria clássica de campos com o objetivo de descrever, simultaneamente, simetrias internas e no espaço-tempo, de maneira unificada. Obtém-se então, nesta linguagem, alguns objetos de estudo centrais da teoria, como os teoremas de Noether e, no caso das teorias de calibre, os teoremas de acoplamento mínimo e Utiyama. Por fim, discute-se brevemente o caso de simetrias a menos de elementos de contato e divergências totais. / The aim of this thesis is to provide a framework that allows the modelling of symmetries in smooth fibre bundles which have good local behaviour. For that, we use Lie groupoids and related tools in order to reduce, whenever possible, symmetries given by the action of a possibly infinite dimensional differentiable group on a smooth fibre bundle to finite dimensional problems. We give a definition of invariance of a differential form, defined on the total space of a fibre bundle, by the action of a Lie groupoid. Then, we discuss these tools in the case of a Lagrangian classical field theory to describe internal and space-time symmetries simultaneously, in a unified way. With this language, we get some central objects of the theory such as Noether\'s theorems and, in the case of gauge theories, the minimal coupling and Utiyama\'s theorems. Lastly, we briefly discuss the case of symmetries up to contact elements and a total divergence.

O objetivo desta tese é oferecer um arcabouço que permita a modelagem de simetrias em fibrados suaves, que possuam um bom comportamento local. Para tanto, usa-se ferramentas de grupoides de Lie e correlatas, com a finalidade de reduzir, quando possível, simetrias dadas pela ação de um grupo diferenciável, possivelmente de dimensão infinita, sobre um fibrado suave, a problemas em dimensão finita. Uma definição de invariância de uma forma diferencial, definida no espaço total de um fibrado suave, sob a ação de um grupoide de Lie, é apresentada e desenvolvida. A seguir, discute-se estas ferramentas no contexto da formulação lagrangiana da teoria clássica de campos com o objetivo de descrever, simultaneamente, simetrias internas e no espaço-tempo, de maneira unificada. Obtém-se então, nesta linguagem, alguns objetos de estudo centrais da teoria, como os teoremas de Noether e, no caso das teorias de calibre, os teoremas de acoplamento mínimo e Utiyama. Por fim, discute-se brevemente o caso de simetrias a menos de elementos de contato e divergências totais. / The aim of this thesis is to provide a framework that allows the modelling of symmetries in smooth fibre bundles which have good local behaviour. For that, we use Lie groupoids and related tools in order to reduce, whenever possible, symmetries given by the action of a possibly infinite dimensional differentiable group on a smooth fibre bundle to finite dimensional problems. We give a definition of invariance of a differential form, defined on the total space of a fibre bundle, by the action of a Lie groupoid. Then, we discuss these tools in the case of a Lagrangian classical field theory to describe internal and space-time symmetries simultaneously, in a unified way. With this language, we get some central objects of the theory such as Noether\'s theorems and, in the case of gauge theories, the minimal coupling and Utiyama\'s theorems. Lastly, we briefly discuss the case of symmetries up to contact elements and a total divergence.

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This paper presents the Lie-Backlund symmetry method to give the equivalence between differential equations and describe the equivalent transformation procedure of nonlinear control systems of partial differential equations. The equivalent linear systems found by solving the infinitesimal generator of one-parameter Lie groups with prolongations and the infinitesimal generator are used to construct the parameters of invertible mapping u. And the equivalence linear form of the nonlinear system is constructed via u. Some necessary conditions for mapping a nonlinear control system of PDE¡¦s to a linear control system of PDE¡¦s are discussed, and application of Lie-Backlund symmetries and invertible mapping u constructed linear time-invariant control system of partial differential equations.

This thesis investigates the topology and geometry of hyperbolic knot complements that are commensurable with other knot complements. In chapter 3, we provide an infinite family examples of hyperbolic knot complements commensurable with exactly two other knot complements. In chapter 4, we exhibit an obstruction to knot complements admitting exceptional surgeries in conjunction with hidden symmetries. Finally, in chapter 5, we discuss the role of surfaces embedded in 3-orbifolds as it relates to hidden symmetries. / text

This thesis studies the symmetries and phenomenologies of the massive vector fields of indefinite spin with both scalar and spin-one degrees of freedom and Elko. The investigation is conducted by using and extending the quantum field theory formalism developed by Wigner and Weinberg. In particular, we explore the possibility that the W± and Z bosons have an additional scalar degree of freedom and show that Elko is a fermionic dark matter candidate. We show that the massive vector fields of indefinite spin are consistent with Poincaré symmetry and have physically desirable properties that are absent for their pure spin-one counterpart. Using the new vector fields, the decay of the W± and Z bosons to leptons at tree-level are in agreement with the Standard Model (SM) predictions. For higher order scattering amplitudes, the theory has better convergent behaviour than the intermediate vector boson model and the Fermi theory. Elko has the unusual property that it satisfies the Klein-Gordon but not the Dirac equation and has mass dimension one instead of three-half. We show that the Elko fields are local only along a preferred axis and that they violate Lorentz symmetry. Motivated by the results obtained by Ahluwalia and Horvath that the Elko spin-sums are covariant under very special relativity (VSR) transformations, we derive the VSR particle states and quantum fields. We show that the VSR particles can only interact with the SM particles through gravity and massive scalar particles thus making them and hence Elko dark matter candidates.

The initial chapter of the thesis provides a review of Weinberg’s formalism for the derivation of quantum fields. The formalism is extended to allow for the derivation of quantum fields with more than one spin degree of freedom. It is conjectured that it may be possible to construct massive bosonic quantum field theories of any desired spin j that are consistent and unitary at all energies without the need for regulator terms by including j + 1 spin degrees of freedom: j, j - 1, down to j - j. The concept is then demonstrated in two subsequent chapters by the derivation of a quantum field with spin one and spin zero degrees of freedom followed the derivation of a quantum field with spin two, spin one, and spin zero degrees of freedom. Both field theories are found to be consistent and unitary at all energies without the need for regulator terms. The final two chapters are on unrelated topics. The penultimate chapter provides an explicit derivation of quantum fields for massless particles of spin one-half. In the final chapter, a derivation of the free-space Proca and Maxwell equations is provided via a consistent identification of the linear combinations of the classical fields of the (1,0) and (0,1) representations of the orthochronous Lorentz group.

A search for B decays to quasi two-body charmless final states involving a pseudoscalar η′ meson recoiling against a K∗ vector meson is described. This thesis primarily describes the analysis of two of the six possible decay channels, with the other four channels necessarily included as the subdecay modes are combined to give an overall branching fraction measurement. The method of analysis is a multivariate maximum likelihood fit for each subdecay channel. The likelihood curves for both modes are then combined, firstly with two other charged modes to yield an overall charged result, and finally the four charged modes are combined with two neutral modes to give an overall branching fraction and significance for the decay channel B → η′K∗. All results use the full Run 1 to Run 4 datasets, comprising 210.5 fb−1 of data, equivalent to 232 million BB pairs, gathered by the BABAR detector at Stanford Linear Accelerator Center in Menlo Park, California. The measured branching fractions and upper limits at 90% confidence limit (CL) are: B(B+ → η′ηππK∗+ K+π0) < 9.5 × 10−6B(B+ → η′ργK∗+ K+π0) < 22 × 10−6.The four-mode combined fit determined the branching fraction for the decay B+ → η′K∗+: B(B+ → η′K∗+) < 7.9 × 10−6. The six-mode combined fit determined the branching fraction for the decay B → η′K∗: B(B → η′K∗) = (4.1 ± 1.0 ± 0.5) × 10−6 at a significance of 5.6 standard deviations.

Orientador: Pedro José Catuogno / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-20T05:04:07Z (GMT). No. of bitstreams: 1 Almeida_LuisRobertoLucingerde_D.pdf: 4124910 bytes, checksum: 249249a4a4959e28b63a5f2e7290a5fe (MD5) Previous issue date: 2012 / Resumo: Nesta tese, estudamos equações diferenciais estocásticas, sob o ponto de vista da teoria das simetrias de Lie. Introduzimos o conceito de simetria de Lie estocástica, que consiste em uma ação que mantém invariante as soluções de uma equação diferencial, onde tal ação é estocástica, isto é, dada por um fluxo estocástico. Nosso principal resultado consiste nas equações de Lie para as simetrias estocásticas, permitindo detectar quando um fluxo estocástico é uma simetria estocástica. Além disso, apresentamos uma possível definição de coordenada canônica para as simetrias estocásticas e obtemos condições, assim como no caso clássico, para encontrá-la. Por fim, mostramos como obter, sistematicamente, transformações entre equações estocásticas / Abstract: In this thesis, we study stochastic differential equations, under the point of view of Lie point symmetries. We introduce the concept of stochastic Lie point symmetry, which consists of an action that keeps invariant the solutions of a differential equation, where such action is stochastic, i.e., given by a stochastic flow. Our main result is the Lie's equations for stochastic symmetries, which allows one to detect when a stochastic flow is a stochastic symmetry. Furthermore, we present a possible definition of canonical coordinates for the stochastic symmetries and we obtain conditions, like in the standard case, to find them. At last, we show how to obtain, systematically, transformations between stochastic differential equations / Doutorado / Matematica / Doutor em Matemática

This thesis deals with two classes of space-time symmetries: emergent symmetries in the near-horizon region of rapidly rotating Kerr black holes and residual gauge symmetries. The main aim of the thesis is to investigate consequences and effects of these symmetries on black holes and gravitational radiation. The first class of symmetries is exploited to address questions of astrophysical relevance for force-free magnetospheres, thin accretion discs, and strong magnetic fields around Kerr black holes. We investigate how the dynamics of electromagnetic and matter fields is constrained by global conformal symmetries of the near-horizon geometry. In the context of force-free electrodynamics, we find exact solutions and classify them according to the highest weight representation of the isometry group. We introduce novel criteria to distinguish physical solutions and deduce bounds on conformal weights of electromagnetic fields. For thin accretion discs, within the Novikov-Thorne model, new properties arise in the high spin regime of the Kerr black hole. We find a novel self-similar solution and we explain the critical behaviour of the observables by symmetry arguments. Afterwards, we study an exact analytic solution to the Einstein-Maxwell theory. It describes a black hole immersed in a strong magnetic field and it shares the same near-horizon geometry of extreme Kerr black holes. We compute its total conserved mass by means of the covariant phase space formalism and study its thermodynamics. The second class of symmetries is considered in order to provide a new definition of gravitational multipole moments by means of Noether charges and by adopting the covariant phase space formalism. We show that such a definition in terms of Noether charges reproduces multipole moments in General Relativity. We propose to apply it to an arbitrary generally covariant metric theory of gravity. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished